Recently the lepton pair production through strong electromagnetic
fields in ultra-peripheral collisions (UPC) has drawn broad interest.
Back to 1930s, Weizsacker and Williams considered the electromagnetic
field produced by a fast moving particle as an equivalent flux of
quasi-real photons [1]}, [2]}.
This approximation is called Weizsacker-Williams method or equivalent
photon approximation (EPA) [3]}. A related process
is the lepton pair production through collisions of two real photons
and was studied by Breit and Wheeler [4]} under the
condition that the total energy of two photons should be greater than
the mass of the lepton pair. The STAR Collaboration at Relativistic
Heavy Ion Collider (RHIC) has measured the lepton pair (\(l\overline{l}\) )
production process in UPC [5]}. There are also several
measurements related to nonlinear effects of quantum electrodynamics
(QED) such as the vacuum birefringence [6]} and the
light-by-light scattering [7]}. The transverse
momentum spectra of the lepton pair in peripheral collisions of heavy
ions are found to be significantly broader than the ones in UPC by
STAR [8]} and by the ATLAS collaboration at the Large
Hadron Collider (LHC) [9]}. Such broadenings may
arise from medium effects in peripheral collisions, therefore, UPC
may provide a baseline for future studies of medium effects.
